The Sun's Mean Line-of-Sight Field

TL;DR

This paper models the Sun's mean magnetic field as a filter for spherical harmonic components, analyzing 46 years of data to understand the origin of different magnetic field parts and their rotational patterns.

Contribution

It introduces a method to interpret solar magnetic field measurements using transmission coefficients for spherical harmonics, revealing the origins of axisymmetric and non-axisymmetric components.

Findings

Non-axisymmetric field originates from specific spherical harmonics.

Power spectrum shows peaks at ~27-day and harmonic periods.

Magnetic patterns exhibit slow rotation due to differential rotation.

Abstract

We regard the Sun-as-a-star magnetic field (i.e. the mean field) as a filter for the spherical harmonic components of the photospheric field, and calculate the transmission coefficients of this filter. The coefficients for each harmonic, $Y_{l}^{m}$, are listed in three tables according to their dependence on $B_{0}$, the observer's latitude in the star's polar coordinate system. These coefficients are used to interpret the 46-yr sequence of daily mean-field measurements at the Wilcox Solar Observatory. We find that the non-axisymmetric part of the field originates in the $Y_{1}^{1}$, $Y_{2}^{2}$, and a combination of the $Y_{3}^{3}$ and $Y_{3}^{1}$ harmonic components. The axisymmetric part of the field originates in $Y_{2}^{0}$ plus a $B_{0}$-dependent combination of the $Y_{1}^{0}$ and $Y_{3}^{0}$ components. The power spectrum of the field has peaks at frequencies corresponding to the ~27-day synodic equatorial rotation period and its second and third harmonics. Each of these peaks has fine structure on its low-frequency side, indicating magnetic patterns that rotate slowly under the influence of differential rotation and meridional flow. The sidebands of the fundamental mode resolve into peaks corresponding to periods of ~28.5 and ~30 days, which tend to occur at the start of sunspot maximum, whereas the ~27-day period tends to occur toward the end of sunspot maximum. We expect similar rotational sidebands to occur in magnetic observations of other Sun-like stars and to be a useful complement to asteroseismology studies of convection and magnetic fields in those stars.